Theory and design for mechanical measurements

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Theory and Design for

Mechanical Measurements

Fifth Edition

Richard S. Figliola

Clemson University

Donald E. Beasley

Clemson University

John Wiley & Sons, Inc.

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Preface

We are pleased to offer this 5th edition of Theory and Design for Mechanical Measurements. This text provides

a well-founded background in the theory of engineering measurements. Integrated throughout are the necessary

elements for the design of measurement systems and measurement test plans, with an emphasis on the role of

statistics and uncertainty analyses in design. The measurements field is very broad, but through careful

selection of the topical coverage we establish the physical principles and practical techniques for many

engineering applications while keeping page count and text cost manageable. Our aim is not to offer a manual

for instrument construction and assembly. Instead, we develop the conceptual design framework for selecting

and specifying equipment and test procedures and for interpreting test results, which we feel are necessary and

common bases for the practice of test engineering. The text is appropriate for undergraduate and graduate level

study in engineering, but is also suitably advanced and oriented to serve as a reference source for professional

practitioners. The pedagogical approach invites independent study or use in related fields requiring an

understanding of instrumentation and measurements.

The organization of the text develops from our view that certain aspects of measurements can be

generalized, such as test plan design, signal analysis and reconstruction, and measurement system response.

Topics such as statistics and uncertainty analysis require a basic development of principles but are then best

illustrated by integrating these topics throughout the text material. Other aspects are better treated in the context

of the measurement of a specific physical quantity, such as strain or temperature.

PEDAGOGICAL TOOLS TO AID LEARNING

In this textbook:

Each chapter begins by defining a set of learning outcomes.

The text develops an intuitive understanding of measurement concepts with its focus on test system

modeling, test plan design, and uncertainty analysis.

Each chapter includes carefully constructed example problems that illustrate new material and

problems that build on prior material.

Each example makes use of a KNOWN, FIND, SOLVE approach as an organizational aid to a

problem’s solution. This methodology for problem solutions helps new users to link words and concepts

with symbols and equations. Many problems contain COMMENTS that expand on the solution,

provide a proper context for application of the principle, or offer design application insight.

End-of-Chapter practice problems are included for each chapter to exercise new concepts.

Practice problems range from those focused on concept development, to building of advanced skills,

to open-ended design applications.

With each chapter, we have added new practice problems but have substantially ‘‘refreshed’’ many

problems from previous editions.

We provide a detailed Instructors Manual for instructors who have adopted the book. We have

carefully reviewed the solutions in this edition to minimize typographical and arithmetical errors. The

manual is available on-line at the Wiley Instructor’s website.

Answers to selected problems will be posted on the Wiley website.

Use of the software in problem solving allows in-depth exploration of key concepts that would be

prohibitively time consuming otherwise. The text includes on-line access to interactive software of

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focused examples based on software using National Instruments Labview1 for exploring some of the

text concepts, while retaining our previous efforts using Matlab1. The Labview programs are available

as executables so they can be run directly without a Labview license. The software is available on both

the Wiley Student and Instructor’s websites.

NEW TO THIS 5TH EDITION

With this 5th edition, we have new or expanded material on a number of topics. As highlights:

We introduce Monte Carlo simulation methods in Chapter 4 and tie their use with uncertainty estima￾tions in Chapter 5.

Treatment of uncertainty analysis in Chapter 5 has been updated to include changes in test standards

methodology relative to ASME PTC 19.1 Test Uncertainty and the International Standards Organization

(ISO) Guide to Uncertainty in Measurements. These changes have been carried into the other chapters

both in language and in example problems. Where we deviate from the methodology of the Standards,

we do so for pedagogical reasons.

Discussion has been added on using rectangular (uniform) distributions in uncertainty estimation.

The treatment of non-symmetric uncertainty intervals and methods for treating correlated errors in

Chapter 5 has been expanded and revisited in other chapters.

We have updated our symbol usage for closer consistency with the standards.

We have added a section presenting image acquisition and processing using digital techniques in

Chapter 7.

We have changed our presentation of pressure transmission line effects to make better use of the lumped

parameter methods of Chapter 3 that engineering students are familiar with, including discussion of the

ideal elements of inertance, resistance, and compliance.

We have revised our treatment of Butterworth filters, including added coverage, in Chapter 6.

Wehaveaddedanintroductiontotheanalysisofstraingaugedatatocomputeprincipal stressesinChapter11.

SUGGESTED COURSE COVERAGE

To aid in course preparation, Chapters 1 through 5 provide an introduction to measurement theory with statistics

and uncertainty analysis, Chapters 6 and 7 provide a broad treatment of analog and digital sampling methods,

and Chapters 8 through 12 are instrumentation focused.

Many users report to us that they use different course structures, so many that it makes a preferred order of

topical presentation difficult to anticipate. To accommodate this, we have written the text in a manner that allows

any instructor to customize the order of material presentation.While the material of Chapters 4 and 5 are integrated

throughout the text and should be taught in sequence, the other chapters tend to stand on their own. The text is

flexible and can be used in a variety of course structures at both the undergraduate and graduate levels.

For a complete measurements course, we recommend the study of Chapters 1 through 7 with use of the

remaining chapters as appropriate. For a lab-course sequence, we recommend using chapters as they best

illustrate the course exercises while building complete coverage over the several lab courses normally within a

curriculum. The manner of the text allows it to be a resource for a lab-only course with minimal lecture. Over

the years, we have used it in several forums, as well as professional development courses, and simply rearrange

material and emphasis to suit the audience and objective.

We express our sincerest appreciation to the students, teachers, and engineers who have used our earlier

editions. We are indebted to the many who have written us with their constructive comments and encouragement.

Richard S. Figliola

Donald E. Beasley

Clemson, South Carolina

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Contents

1 Basic Concepts of Measurement Methods 1

1.1 Introduction 1

1.2 General Measurement System 2

1.3 Experimental Test Plan 6

1.4 Calibration 15

1.5 Standards 23

1.6 Presenting Data 30

1.7 Summary 31

References 31

Nomenclature 32

Problems 32

2 Static and Dynamic Characteristics of Signals 41

2.1 Introduction 41

2.2 Input/Output Signal Concepts 41

2.3 Signal Analysis 46

2.4 Signal Amplitude And Frequency 49

2.5 Fourier Transform and The Frequency Spectrum 63

2.6 Summary 71

References 71

Suggested Reading 71

Nomenclature 72

Problems 72

3 Measurement System Behavior 79

3.1 Introduction 79

3.2 General Model for a Measurement System 79

3.3 Special Cases of the General System Model 83

3.4 Transfer Functions 104

3.5 Phase Linearity 106

3.6 Multiple-Function Inputs 107

3.7 Coupled Systems 109

3.8 Summary 111

References 111

Nomenclature 111

Problems 112

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4 Probability and Statistics 118

4.1 Introduction 118

4.2 Statistical Measurement Theory 119

4.3 Describing the Behavior of a Population 125

4.4 Statistics of Finite-Sized Data Sets 129

4.5 Chi-Squared Distribution 135

4.6 Regression Analysis 139

4.7 Data Outlier Detection 147

4.8 Number of Measurements Required 148

4.9 Monte Carlo Simulations 150

4.10 Summary 152

References 152

Nomenclature 153

Problems 153

5 Uncertainty Analysis 161

5.1 Introduction 161

5.2 Measurement Errors 162

5.3 Design-Stage Uncertainty Analysis 164

5.4 Identifying Error Sources 168

5.5 Systematic and Random Errors 170

5.6 Uncertainty Analysis: Error Propagation 172

5.7 Advanced-Stage Uncertainty Analysis 176

5.8 Multiple-Measurement Uncertainty Analysis 182

5.9 Correction for Correlated Errors 195

5.10 Nonsymmetrical Systematic Uncertainty Interval 197

5.11 Summary 198

References 199

Nomenclature 199

Problems 200

6 Analog Electrical Devices and Measurements 209

6.1 Introduction 209

6.2 Analog Devices: Current Measurements 210

6.3 Analog Devices: Voltage Measurements 214

6.4 Analog Devices: Resistance Measurements 219

6.5 Loading Errors and Impedance Matching 226

6.6 Analog Signal Conditioning: Amplifiers 230

6.7 Analog Signal Conditioning: Special-Purpose Circuits 234

6.8 Analog Signal Conditioning: Filters 239

6.9 Grounds, Shielding, and Connecting Wires 250

6.10 Summary 252

References 253

Nomenclature 253

Problems 254

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7 Sampling, Digital Devices, and Data Acquisition 260

7.1 Introduction 260

7.2 Sampling Concepts 261

7.3 Digital Devices: Bits and Words 269

7.4 Transmitting Digital Numbers: High and Low Signals 271

7.5 Voltage Measurements 271

7.6 Data-Acquisition Systems 283

7.7 Data-Acquisition System Components 284

7.8 Analog Input-Output Communication 288

7.9 Digital Input-Output Communication 293

7.10 Digital Image Acquisition and Processing 299

7.11 Summary 303

References 303

Suggested Reading 304

Nomenclature 304

Problems 305

8 Temperature Measurements 309

8.1 Introduction 309

8.2 Temperature Standards and Definition 310

8.3 Thermometry Based on Thermal Expansion 313

8.4 Electrical Resistance Thermometry 315

8.5 Thermoelectric Temperature Measurement 330

8.6 Radiative Temperature Measurements 351

8.7 Physical Errors in Temperature Measurement 356

8.8 Summary 365

References 365

Nomenclature 366

Problems 367

9 Pressure and Velocity Measurements 375

9.1 Introduction 375

9.2 Pressure Concepts 375

9.3 Pressure Reference Instruments 378

9.4 Pressure Transducers 386

9.5 Pressure Transducer Calibration 392

9.6 Pressure Measurements in Moving Fluids 396

9.7 Modeling Pressure and Fluid Systems 400

9.8 Design and Installation: Transmission Effects 401

9.9 Fluid Velocity Measuring Systems 405

9.10 Summary 415

References 416

Nomenclature 417

Problems 417

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10 Flow Measurements 423

10.1 Introduction 423

10.2 Historical Background 423

10.3 Flow Rate Concepts 424

10.4 Volume Flow Rate Through Velocity Determination 425

10.5 Pressure Differential Meters 427

10.6 Insertion Volume Flow Meters 446

10.7 Mass Flow Meters 454

10.8 Flow Meter Calibration and Standards 459

10.9 Estimating Standard Flow Rate 460

10.10 Summary 461

References 461

Nomenclature 462

Problems 462

11 Strain Measurement 466

11.1 Introduction 466

11.2 Stress and Strain 466

11.3 Resistance Strain Gauges 469

11.4 Strain Gauge Electrical Circuits 476

11.5 Practical Considerations for Strain Measurement 479

11.6 Apparent Strain and Temperature Compensation 482

11.7 Optical Strain Measuring Techniques 492

11.8 Summary 497

References 498

Nomenclature 498

Problems 499

12 Mechatronics: Sensors, Actuators, and Controls 504

12.1 Introduction 504

12.2 Sensors 504

12.3 Actuators 534

12.4 Controls 540

12.5 Summary 557

Nomenclature 558

References 558

Problems 559

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Appendix A A Guide for Technical Writing 563

A Guide For Technical Writing 563

References 568

Appendix B Property Data and Conversion Factors 569

Appendix C Laplace Transform Basics 576

C.1 Final Value Theorem 577

C.2 Laplace Transform Pairs 577

References 577

Glossary 578

Index 585

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Chapter 1

Basic Concepts of Measurement

Methods

1.1 INTRODUCTION

We make measurements every day. Consider the common measurements illustrated in Figure 1.1.

We routinely read the temperature of an outdoor thermometer to choose appropriate clothing for

the day. We expect to have exactly 10 gallons or liters of fuel added to our tank when that volume

is indicated on a fuel pump. And we expect measuring cups to yield correct quantities of

ingredients in cooking. We put little thought into the selection of instruments for these routine

measurements. After all, the direct use of the data is clear to us, the type of instruments and

techniques are familiar to us, and the outcome of these measurements is not important enough to

merit much attention to features like improved accuracy or alternative methods. But when the

stakes become greater, the selection of measurement equipment and techniques and the interpre￾tation of the measured data can demand considerable attention. Just contemplate how you might

verify that a new engine is built as designed and meets the power and emissions performance

specifications required.

But first things first. The objective in any measurement is to answer a question. So we take

measurements to establish the value or the tendency of some variable, the results of which are

specifically targeted to answer our question. The information acquired is based on the output of the

measurement device or system. There are important issues to be addressed to ensure that the output

of the measurement device is a reliable indication of the true value of the measured variable. In

addition, we must address the following important questions:

1. How can a measurement or test plan be devised so that the measurement provides the

unambiguous information we seek?

2. How can a measurement system be used so that the engineer can easily interpret the

measured data and be confident in their meaning?

There are procedures that address these measurement questions.

At the onset, we want to stress that the subject of this text is real-life oriented. Specifying a

measurement system and measurement procedures represents an open-ended design problem whose

outcome will not have one particular solution. That means there may be several approaches to

solving a measurement problem, and some will be better than others. This text emphasizes accepted

procedures for analyzing a measurement problem to assist in the selection of equipment,

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methodology, and data analysis to meet the design objectives. Perhaps more than in any other

technical field, the approach taken in measurement design and the outcome achieved will often

depend on the attention and experience of the designer.

Upon completion of this chapter, the reader will be able to

identify the major components of a general measurement system, and state the function of

each,

develop an experimental test plan,

distinguish between random and systematic errors,

describe and define the various error types,

define a standard and distinguish among primary, secondary, and transfer standards, and

clearly delineate defined and derived dimensions in various unit systems.

1.2 GENERAL MEASUREMENT SYSTEM

A measurement1 is an act of assigning a specific value to a physical variable. That physical variable

is the measured variable. A measurement system is a tool used for quantifying the measured

variable. As such, a measurement system is used to extend the abilities of the human senses that,

while they can detect and recognize different degrees of roughness, length, sound, color, and smell,

are limited and relative; they are not very adept at assigning specific values to sensed variables.

A system is composed of components that work together to accomplish a specific objective. We

begin by describing the components that make up a measurement system, using specific examples.

Then we will generalize to a model of the generic measurement system.

Figure 1.1 Common devices that

involve measurements.

1 There are many new engineering measurement terms introduced. A glossary of the italicized terms is located in the back of

the text for your reference.

2 Chapter 1 Basic Concepts of Measurement Methods

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Sensor and Transducer

An increasingly important area of scientific inquiry is the characteristics of matter at the nanoscale.

Suppose we want to measure the profile of a surface at a nanometer scale. We discover that a small

(very small) cantilever beam placed near the surface is deflected by atomic forces. Let’s assume for

now that they are repulsive forces. If this cantilever is translated over the surface, the cantilever will

deflect, indicating the height of the surface. This concept is illustrated in Figure 1.2; the device is

called an atomic force microscope. The cantilever beam is a sensor, a physical element that employs

some natural phenomenon, in this case deflection under the action of a force, to sense the variable

being measured, in this case the height of the surface.

So, we have a sensor to measure at the nanometer scale. But we have no means of getting an output

from the sensor that we can record. Suppose that the upper surface of the cantilever is reflective, and we

shine a laser onto the upper surface, as shown in Figure 1.3. The movement of the cantilever will deflect

the laser. Employing a number of light sensors, also shown in Figure 1.3, the deflection of the laser can

be sensed and that deflection corresponds to the height of the surface. Together the laser and the light

sensors (photodiodes) form the transducer component of the measurement system. A transducer

converts the sensed information into a detectable signal. The signal might be mechanical, electrical,

optical, or may take any other form that can be meaningfully recorded.

We should note that sensor selection, placement, and installation are particularly important to

ensure that the sensor output accurately reflects the measurement objective. The familiar phrase

Cantilever and tip

Sample surface Figure 1.2 Sensor stage of an atomic-force

microscope.

Cantilever and tip

Photodiodes

Laser

Sample surface

Detector and

feedback

electronics

Figure 1.3 Atomic-force microscope with

sensor and transducer stages.

1.2 General Measurement System 3